Understanding Binomial Tests: Hypothesis Testing & Analysis

Lab 5: Binomial Tests Winter 2023 – van Hees Learning outcomes:  practice stating null and alternative hypotheses  practice making probability distributions for the null hypothesis  practice calculating P values of the PDF and CDF functions using dbinom() and pbinom() Lab write-up: fill in your answers for the questions on this handout. Turn it in to canvas as a PDF. Problem 1: Scientist that work for a Dutch company that sells tulip bulbs have been breeding a population of tulips that have a bright purple color that is rare in the natural population. Because these purple tulips are rare, they are charging more for these tulip bulbs. The company scientists make a genetic model that xpredicts that .35 of a population of tulips will have purple flowers. A farmer in the Skagit Valley buys a crate of these special, and expensive tulips from the Netherlands, but she is skeptical that the company’s estimate of 35% of the purple flowers, because last year she didn’t get that many and suspects that it’s less than .35. You select 50 random bulbs from a large bin and plant the blubs in the fall. In the spring, with the tulips bloom, you count 11 purple flowers. Is there enough evidence now that the rate of purple flowers in this population is less than .35? 1) H o = H a = General Rules for Hypothesis Testing 1) Define H o and H a 2) Determine which probability distribution to use and plot the null distribution 3) Determine Parameters of test 4) Run test 5) Interpret results

2) Probability distribution: R script = Copy and paste in the probability distribution under the null hypothesis 3) Calculate the p value using dbinom() R script: 4) Calculate the p value using pbinom() R script: 5) Run the test using binom.test() R script: P-value: 6) Can you reject the null hypothesis?

Problem 2: A strain of inbred mice has a form of muscular dystrophy that has a clear genetic basis. The probability of appearance of this issue in any one mouse born of a set of specified parents is ¼. If 20 offspring are raised by these parents, find the following probabilities: a) fewer than 5 will have muscular dystrophy b) exactly 5 will have muscular dystrophy c) fewer than 8 will have muscular dystrophy In the same strain of mice, you determine that the appearance of muscular dystrophy is often accompanied with a change in coat color, but you have no idea if this change in color has a genetic bases or what kind of genetic basis. You want to do a test with your existing data to decide if it was possible that changes in coat color were random. Twenty two of 50 mice with muscular dystrophy had a grey coat, all other mice in that population have a white coat. How would you set up and run this test? 1) H o = H a = 2) Probability distribution: R script = Sketch the graph of probability distribution (or copy and paste it in): 3) Run the test using binom.test() R script:

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P-value: 4) Calculate the p value using dbinom() R script: 5) Calculate the p value using pbinom() R script: 6) Can you reject the null hypothesis? 7) Is coat color random in the muscular dystrophy population?

23W 340 Lab 5 - Bionomial Tests

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